I think it depends on the club / predicament; if a club is in a relegation battle then yes the new manager needs to change the fortunes immediately. However at clubs like MU realistically the worst case scenario is they finish in mid-table mediocrity (similar to Chelsea a few seasons ago) so there is an argument that it is best to get the new manager in mid-season as he then basically barring almighty ****-up gets a 'free pass' for this season and can use the time to start assessing the squad, getting his ideas across, identifying targets for the transfer windows etc. Whereas if they come in during the summer they have much less time to sort all that out, or worse some players could have already made their mind up to look for a move by that point.
I accept there is perhaps a risk that they lose some players during the part-season but I also think if Mourinho sticks around you could see e.g. Pogba sorting out his next move, Rashford angling for something to happen etc. It's also arguably better to lose the players in the second half of this season and then have an opportunity to rebuild in the summer, than lose the players at the start of next season and have two seasons messed up instead of one.
There may be a big penalty for not being in the CL as well though - a while ago there were loads of articles that Chevy would pay a lot less sponsorship if Utd didn't qualfy twice for the CL - now the way it was written in majority of articles I read at the time - didn't say explicitly that it was two years in a row (they didn't say either way, whether it was "in a row" or "two years during any time during the length of the deal" so it could be either one.
You may well say Utd are looking unlikely to make it either way, but at least sacking him now would give the incoming manager a decent chance to make top 4 before the end of the season......and he would also get a good idea by Jan who he could sell immediately and who if anyone he could bring in (even if its only one "leader" in defence that would make a massive improvement) .
There are massive problems throughout the club, from the owners all the way down to the inadequate squad. Everyone is to blame for the mess but imo particularly the Glazers & Woodward for being more about the finance and financial aspect (of what they can get out of the club ) rather than being interested in the actual football - after all if the football is actually good quality that will look after the finance anyway, their way doesn't always and in this case definitely hasn't worked.
JM hasn't helped himself in many ways but there was an interesting stat I heard the other day that the glazers have paid far more out to themselves and in financing their takeover than they have in players since that date. Just shows why we haven't grown as much ( the Glazers started building up the marketing side really well, credit to them- but as many clubs have now caught up ....kinda shows how this aspect of the growth has massively slowed since the initial push).
Any manager is going to be a risk - but I guess at least ZZ has decent experience of a club of a similar size, a lot of managers would be daunted by the sheer size and we will still be in the same position 2 years from now. Im not sure whether ZZ would improve the current squad enough (even with one or two additions in Jan) - unqualified success in CL at RM no doubt, but he had an absolute stellar squad there when he arrived. Not including some of the dregs of the overpayed dregs of the PL .
edit - I would get rid of Sanchez straight away, he just isn't cutting it no matter how / where we play him. (incredibly costly no doubt but I don't see any manager getting the 20 goals a season + we should be getting out of him)
Get Martial / Rashford alternating on the left wing - will give them both plenty of minutes and was working a treat for both of them last year . Do need a proper right winger for the other side though (alternating with Periera perhaps, was originally a winger / no 10 so might do this well)
I wouldn't actually mind seeing Delot as a right winger (if we had a better defender behind him of course) , his pace and crossing would be brilliant without concern of whats happening behind him - and at some point we will need to alternate with him anyway